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VARIETIES GENERATED BY COMPLETELY 0-SIMPLE SEMIGROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 84 / Issue 3 / June 2008
- Published online by Cambridge University Press:
- 01 June 2008, pp. 375-403
- Print publication:
- June 2008
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- Article
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Kublanovsky has shown that if a subvariety V of the variety RSn generated by completely 0-simple semigroups over groups of exponent n is itself generated by completely 0-simple semigroups, then it must satisfy one of three conditions: (i) A2 ∈ V; (ii)
(iii) B2∈V but 
The conditions (i) and (ii) are also sufficient conditions. In this note, we complete Kublanovsky’s programme by refining condition (iii) to obtain a complete set of conditions that are both necessary and sufficient.
(iii) 
The conditions (i) and (ii) are also sufficient conditions. In this note, we complete Kublanovsky’s programme by refining condition (iii) to obtain a complete set of conditions that are both necessary and sufficient.